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<h1 class="reftitle">minus</h1>
<h2>Purpose</h2>
<p>Subtract a Polyhedron or a vector from a Polyhedron.</p>
<h2>Syntax</h2>
<pre class="synopsis">Q = P - S</pre>
<pre class="synopsis">Q = minus(P,S)</pre>
<pre class="synopsis">Q = P - x</pre>
<pre class="synopsis">Q = minus(P, x)</pre>
<h2>Description</h2>
<p></p>
    Compute the Pontryagin difference of <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus1.png"> and <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus2.png">, or <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus3.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus3.png"> and <img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus4.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus4.png">.
    <p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus5.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus5.png"></p>
    or
    <p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus6.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus6.png"></p>
  
   <h2>Input Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
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<col width="31%">
<col width="69%">
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<td><tt>P</tt></td>
<td>
<p></p>Polyhedron in any format<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>S</tt></td>
<td>
<p></p>Polyhedron in any format<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr>
<tr valign="top">
<td><tt>x</tt></td>
<td>
<p></p>Column vector of length <tt>P.Dim</tt>
      <p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr>
</tbody>
</table>
<h2>Output Arguments</h2>
<table cellspacing="0" class="body" cellpadding="4" border="0" width="100%">
<colgroup>
<col width="31%">
<col width="69%">
</colgroup>
<tbody><tr valign="top">
<td><tt>Q</tt></td>
<td>
<p></p>Polyhedron <tt>Q = P-S</tt> or <tt>Q = P-x</tt>.<p>
	    		Class: <tt>Polyhedron</tt></p>
</td>
</tr></tbody>
</table>
<h2>Example(s)</h2>
<h3>Example 
				1</h3>Subtract one polytope from another<pre class="programlisting">P = Polyhedron('H',[sin([0:0.5:2*pi])' cos([0:0.5:2*pi])' ones(13,1)]);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S = Polyhedron('lb',[-1;-1]*0.1,'ub',[1;1]*0.1);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">Q = P-S;</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">P.plot('color','b'); hold on;
	Q.plot('color','g');
	S.plot('color','r');</pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_1.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_1.png" width="60%"></p>
<h3>Example 
				2</h3>Subtract a line segment from a polytope<pre class="programlisting">P = Polyhedron('H',[sin([0:0.5:2*pi])' cos([0:0.5:2*pi])' ones(13,1)]);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S = Polyhedron('V', 0.1*[-1 1;1 -1]);</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">Q = P-S;</pre>
<pre class="programlisting"></pre>
<pre class="programlisting">P.plot('color','b'); hold on;
	 Q.plot('color','r');
	 S.plot('color','g','linewidth',2);</pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_2.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_2.png" width="60%"></p>
<h3>Example 
				3</h3>Unbounded polyhedron minus lower-dimensional polytope<pre class="programlisting">P = Polyhedron('lb',-[1;1;1]*0.5,'ub',[1;1;1]*0.5,'He',[randn(1,3) 0.1]); </pre>
<pre class="programlisting"></pre>
<pre class="programlisting">S = Polyhedron('V',randn(10,3),'R',[1 1 1])+[1;1;1]; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting">Q = S-P; </pre>
<pre class="programlisting"></pre>
<pre class="programlisting">P.plot('color', 'g'); hold on;
	 S.plot('color', 'b');
	 Q.plot('color','r');
    </pre>
<pre class="programlisting"></pre>
<p class="programlistingindent"><img src="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_3.png" alt="../../../../../../fig/mpt/modules/geometry/sets/@Polyhedron/minus_img_3.png" width="60%"></p>
<h2>See Also</h2>
<a href="./plus.html">plus</a><p></p>
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<br><p>©  <b>2010-2013</b>     Colin Neil Jones: EPF Lausanne,    <a href="mailto:colin.jones@epfl.ch">colin.jones@epfl.ch</a></p>
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